The ergodic limit of multipass absorption for fast wave current drive in tokamaks

In many parameter regimes of interest for fast wave current drive (FWCD) in tokamaks, direct absorption of the fast wave by resonant electrons is a weak process and multipass absorption is an important issue. Although both full wave codes and ray tracing codes have been developed to model FWCD, in the multipass regime these tools are computationally intensive, and yield little insight into the nature of the solutions. In this work, an alternative approach is considered. Based on the wave kinetic equation, a natural limit emerges for the multipass regime, where wave energy density, convected along stochastic ray trajectories, uniformly fills the entire accessible phase space. In this ergodic, weak damping limit, the absorbed power density and corresponding wave-driven current density are readily obtained by calculating the appropriate set of one-dimensional k-space integrals at every point in configuration space. The method is used here to model FWCD on the DIII-D tokamak [R. I. Pinsker and the DIII-D Team, Plasma Physics and Controlled Nuclear Fusion Research 1992 (International Atomic Energy Agency, Vienna, 1993), Vol. 1, p. 683]. An example for reactor-grade plasma parameters is also considered